Many types of variable stroke mechanisms have been proposed for use in engines to vary the displacement of the pistons. Recently it has again been suggested that variable displacement engines could have advantages over fixed displacement engines in the areas of both emission control and overall efficiency. However, to obtain these advantages it is necessary that the mechanical linkage used to transmit power from the engine pistons to the output shaft itself be arranged to transmit the power in an efficient manner. It is further desirable that the mechanism be balanceable within limits considered acceptable for application in automotive vehicles. U.S. Pat. No. 4,112,826 Cataldo assigned to the assignee of the present invention discloses some examples of engine arrangements proposed to provide some or all of these features.